When Gabriel visited Mary, she was, as is usual when meeting an angel, troubled by it:

In the sixth month the angel Gabriel was sent from God to a city of Galilee named Nazareth, to a virgin betrothed to a man whose name was Joseph, of the house of David. And the virgin's name was Mary. And he came to her and said, “Greetings, O favored one, the Lord is with you!” But she was greatly troubled at the saying, and tried to discern what sort of greeting this might be.—Luke 1:26-29 (ESV)

But it's odd that she should need to interpret what "sort of greeting" Gabriel was bringing to her. Why didn't she understand, without needing any special discernment, that the message was one of good news? Is there some other way that Gabriel's words could have been interpreted?

2 Answers
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Possibly her reaction is more along the lines of shock as she was unable to reconcile the favor implied in the greeting compared to her own humble view of herself. Therefore she tries to discern what it could mean without actually making her 'highly favored'.

For example if the President of a nation stopped buy a peasant and said hello, you shall be my vice president (literally meaning it) the peasant would try to discern what this really meant. Its a kind of 'Say what?!'

@H3br3wHamm3r81 - I assumed the emotion you are adding but good you mention it. She was in disbelief while reverently pondering. It was not a 'Ha, yeah right' at all. That is casual, it is more like in front of a supreme court judge that hammers the gavel in her favor and she says 'What?!' please explain. The fear provides context to the reverent disbelief.
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MikeJan 20 '13 at 0:57

Just a thought, but the husband of her cousin (Elizabeth) was Zecharias, who had just had a similar experience with the very same angel Gabriel several months earlier, and Gabriel had left him (Zecharias) mute. Gabriel's announcement to Zecharias was the birth of John.

Gabriel now appears unannounced to Mary, and indicates that her child will possess the Davidic Covenant (Luke 1:32), so Mary now concludes that she is going to bear the Promised Seed. She asks an honest question, since she is a virgin of course, but after Gabriel's response, she assents and praises the Lord, unlike Zecharias, who had second-guessed Gabriel with cynicism.

Since Mary immediately departed Nazareth and went to the "hill country of Judea" (which is halfway across the land of Israel) to be with Elizabeth, indicates that Mary had correlated the announcement by Gabriel to the announcement by the same angel to Zecharias.